A few living cells do not posses nucleus. These few living cells must have other means of delivering messages. Does this mean they do not have chromosomes Are they also located in the same organism, in this case the animal?

The nucleus consist of a nuclear membrane with holes (pores in them), Inside this membrane there are chromosomes. These chromosomes bunch up to a total of 46 multiple times in a cells lifetime. These contain coded instructions divided in genes. Like a line of code that carries instructions in a cumputer program. These strings of code are sent to the rest of the cell in packages. Those pass through the pores into the cell where they deliver these instructions.

The nucleus carries the genetic information, but in non animal cells where is the genetic material held?